Solve for $x$ and $y$ using elimination. ${x-6y = -28}$ ${-x-5y = -38}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-11y = -66$ $\dfrac{-11y}{{-11}} = \dfrac{-66}{{-11}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {x-6y = -28}\thinspace$ to find $x$ ${x - 6}{(6)}{= -28}$ $x-36 = -28$ $x-36{+36} = -28{+36}$ ${x = 8}$ You can also plug ${y = 6}$ into $\thinspace {-x-5y = -38}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(6)}{= -38}$ ${x = 8}$